My suggestion is to use mouse over event to show/hide the sidebar.
It would save some space on small screens, make sidebar easier to use and less annoying and would improve LibreOffice appearance.
I'm using Libre Office 4.1 on Ubuntu 13.10 from PPA.
Great suggestion - confirming that it's valid
If you remember, we used to have controls that appeared on mouse-over, such as in the header/footer or in the slide pane. This caused a lot of accidental misclicks and thus went against our "ux-error-prevention" principle , so, for the same reasons, an on-hover sidebar is a no-go, I'm afraid.
As implemented for 4.2 onward, the Sidebar has vertical click-able button "Hide" or "Show" that positively achieves this function over a mouse-over fly-out.
Agree with Mierk and find this UX function is more robust.
Closing as won't fix. If folks feel there is still a requirement for mouse-over fly-out treatment of the Sidebar, please reopen but provide reasonable justification of the requirement.
And, actually the "Show" "Hide" function was implemented early in the 4.1 release.